the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 18 minutes, (b) between 22 and 31 minutes, and (c) more than 30 minutes.

Answer:

(5 + 9) + 3 = 17

Step-by-step explanation:

The Associative Property of Addition states that no matter how you group the numbers to be added, the results will still be the same. In this case:

Original:

5 + (9 + 3) = 17

5 + 12 = 17

17 = 17 (True)

Associative Property of Addition:

(5 + 9) + 3 = 17

(14) + 3 = 17

17 = 17 (True)

As you can see, the grouping does not matter as the outcome is still the same.

~

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Answer:

#1. A. y=sin x + 2 Is the same as cos.

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

the solution to a relation (like an equation, but also inequalities and so on) is the set of values that make the whole thing true (or consistent).

every other value is not a solution.

Answer:

False

Step-by-step explanation:

You can transform a function many times

:)

The value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle. For each vertex, there are two equivalent exterior angles.

Each vertex typically displays a single external angle. The exterior angles of a triangle are those that are formed outside of it. The exterior angle of a triangle is defined as the angle formed between one of a triangle's sides and its neighboring extended side. As a result, the exterior angle of a triangle is the angle formed by any extended side of a triangle and its neighboring side.

Given that the measure of angle y = 49 degrees.

We observe from the figure that angle a is vertically opposite angle of y thus,

angle y = angle a = 49 degrees.

Now, angle b is exterior angle and,

angle b = angle a + 90

angle b = 49 + 90

angle b = 139 degrees.

Hence, the value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

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The probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.304.

This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.

Let X be the number of Indianapolis residents in a sample of 30 who wanted the Giants to beat the Patriots. Then X follows a binomial distribution with n = 30 and p = 0.97, since the probability of success (rooting for the Giants) is 0.97 for each resident.

We want to find the probability that fewer than 95% of the sample wanted the Giants to win. That is, we want to find P(X < 0.95*30) = P(X < 28.5), where X has the binomial distribution with parameters n = 30 and p = 0.97.

We can use a continuity correction and approximate this probability by the cumulative distribution function of a normal distribution with mean np and variance np(1-p). That is,

P(X < 28.5) ≈ P(Z < (28.5 - np) / sqrt(np(1-p)))

where Z is a standard normal random variable. Substituting the values of n and p, we get

P(X < 28.5) ≈ P(Z < (28.5 - 300.97) / sqrt(300.97*0.03))

≈ P(Z < -0.51)

Using a standard normal table or calculator, we find that P(Z < -0.51) ≈ 0.304. Therefore, the probability that fewer than 95% of the sample wanted the Giants to win is approximately 0.304.

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The given question is incomplete, the complete question is:

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 97% of Indianapolis residents wanted the Giants to beat the Patriots.

What is the probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?

Answer:

Let the cost of each pair of trousers be x dollars.

(i) Belle bought 40 pairs of trousers for a total of $2040, so we can set up an equation:

40x = 2040

Solving for x, we get:

x = 2040/40 = 51

Therefore, each pair of trousers cost Belle $51 to buy.

(ii) Belle made a loss of $200 on the entire sale of 40 pairs of trousers. The cost of 40 pairs of trousers is:

40 x $51 = $2040

So, Belle sold 40 pairs of trousers for:

$2040 - $200 = $1840

Belle's cost was $2040, and she sold the trousers for $1840, so her loss was:

$2040 - $1840 = $200

The loss per pair of trousers is the total loss divided by the number of pairs of trousers sold, which is:

$200/40 = $5

Therefore, Belle made a loss of $5 on each pair of trousers sold.

(iii) The selling price of each pair of trousers can be found by adding the loss per pair to the cost per pair:

Selling price = Cost + Loss

Selling price = $51 + $5

Selling price = $56

Therefore, Belle sold each pair of trousers for $56.

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By using subtraction of polynomial, The polynomial 5x2y2 - 18xy2 - 10x2y is bigger by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 than -5x2 + 6x2y - 7xy.

To find the difference between 5x^2y^2 - 18xy^2 - 10x^2y and -5x^2 + 6x^2y - 7xy, we simply subtraction of polynomial the second expression from the first expression:

(5x^2y^2 - 18xy^2 - 10x^2y) - (-5x^2 + 6x^2y - 7xy)

= 5x^2y^2 - 18xy^2 - 10x^2y + 5x^2 - 6x^2y + 7xy (distributing the negative sign)

= 5x^2y^2 - 10x^2y + 5x^2 - 18xy^2 - 6x^2y + 7xy (rearranging terms)

= 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 (combining like terms)

Therefore, the expression 5x^2y^2 - 18xy^2 - 10x^2y is bigger than -5x^2 + 6x^2y - 7xy by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2.

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Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.

To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.

First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.

Arranging the data in ascending order

2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53

Q1 = 17

Q2 = 24

Q3 = 43

Next, we can calculate the IQR by subtracting Q1 from Q3

IQR = Q3 - Q1 = 43 - 17 = 26

Now we can calculate the lower and upper bounds

Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8

Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79

Any values outside the lower and upper bounds are considered outliers.

In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.

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To solve a system of equations, you need to find the values of the variables that satisfy both equations simultaneously. There are different methods to solve systems of equations, including substitution, elimination, and graphing. Here's an example of using substitution:

Solve the system of equations:

2x + y = 5

x - y = 1

From the second equation, we get x = y + 1. Substitute this expression for x into the first equation:

2(y + 1) + y = 5

Simplifying and solving for y, we get:

3y + 2 = 5

3y = 3

y = 1

Then, substitute y = 1 into x = y + 1 to get:

x = 2

So the solution to the system of equations is x = 2 and y = 1.

To solve a system of inequalities, you need to find the values of the variables that satisfy both inequalities simultaneously. There are different methods to solve systems of inequalities, including graphing and substitution. Here's an example of using graphing:

Solve the system of inequalities:

x + y ≤ 3

x - y > 1

First, graph the boundary lines of each inequality. For the first inequality, the boundary line is x + y = 3, which is a line with intercepts (3, 0) and (0, 3). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 + 0 ≤ 3, which is true

Therefore, shade the side of the line that contains the origin.

For the second inequality, the boundary line is x - y = 1, which is a line with intercepts (1, 0) and (0, -1). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 - 0 > 1, which is false

Therefore, shade the side of the line that does not contain the origin.

The shaded region that satisfies both inequalities is the region that is below the line x + y = 3 and to the right of the line x - y = 1. This region is a triangle with vertices (1, 2), (2, 1), and (2, 2).

I hope this explanation helps you with your homework!

Answer:

Mode = 25

Median = 29

Mean = 30.3

Range = 36

Step-by-step explanation:

To find the mode, order the numbers lowest to highest and see which number appears the most often.

To find the median, calculate the mean by adding together the middle values and dividing them by two.

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.

Answer:

168 ft^2

Step-by-step explanation:

18×8=144ft^2 for the area of the rectangle

8×6=48ft^2

48÷2=24ft^2 for the area of the triangle

144+24=168ft^2

the answer will be 3675.0 m (rounded to one decimal place)

What is rounded off?

Rounding off is a process of approximating a number to a certain degree of accuracy. When we round off a number, we usually need to specify the number of digits we want to keep or the position to which we want to round.

For example, if we want to round off 3.14159 to two decimal places, we would look at the third decimal place (which is 1) and see that it is less than 5, so we would keep the first two decimal places and round off the rest. Thus, rounding off 3.14159 to two decimal places would give us 3.14.

Rounding off is often used to simplify numbers or make them easier to work with, especially in situations where exact values are not necessary or practical.

To round 3675 m to the nearest tenth of a meter, we need to look at the hundredth digit, which is 7. Since 7 is greater than or equal to 5, we need to round up the last digit (tenth digit). Therefore, rounding 3675 m to the nearest tenth of a meter gives us:

Hence the answer will be 3675.0 m (rounded to one decimal place).

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The factorizations of the given expressions are:

[tex]9x^{2}-6x+15[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex] = 10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex] = (x+4)(x-4)

[tex]9x^{2}-6x+15[/tex]

We can first factor out the greatest common factor, 3:

[tex]9x^{2}-6x+15[/tex] = 3([tex]3x^{2}-2x-5[/tex])

[tex]3x^{2}-2x-5[/tex] = (3x+5)(x-2)

Putting it all together, we get:

[tex]9x^{2}-6x+5[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex]

We need to find two numbers that multiply to give 2x5=10 and add up to 11. Those numbers are 1 and 10:

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex]

We need to find two numbers that multiply to give 2x(-9)=-18 and add up to 3. Those numbers are 6 and -3:

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex]

We can first simplify the expression by factoring out 10:

[tex]10x^{2}+80x+70[/tex] = 10([tex]x^{2}+8x+7[/tex])

Now we need to factor the quadratic expression inside the parentheses:

[tex]x^{2}+8x+7[/tex] = (x+1)(x+7)

Putting it all together, we get:

10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex]

We need to find two numbers that multiply to give 3x4=12 and add up to -8. Those numbers are -2 and -6:

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex]

This is a difference of squares, which we can factor as:

[tex]x^{2}-16[/tex] = (x+4)(x-4)

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Answer:

Each black pentagon in the soccer ball is surrounded by five white hexagons. Each white hexagon is, in turn, surrounded by three black pentagons and three other white hexagons. This pattern is repeated throughout the soccer ball.

To find the measures of the angles of the shapes that make the soccer ball, we need to first consider the angles of a regular pentagon and a regular hexagon.

A regular pentagon has five sides and five angles that are equal in measure. The formula for finding the measure of each angle in a regular pentagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular pentagon, n=5. Therefore, the measure of each angle in a regular pentagon is:

(angle measure) = (180(5-2))/5 = 108 degrees.

A regular hexagon has six sides and six angles that are equal in measure. The formula for finding the measure of each angle in a regular hexagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular hexagon, n=6. Therefore, the measure of each angle in a regular hexagon is:

(angle measure) = (180(6-2))/6 = 120 degrees.

Now, let's consider the angles of the shapes that make up the soccer ball.

Each black pentagon has five angles that are equal in measure. Therefore, each angle in a black pentagon measures:

(angle measure) = (180(5-2))/5 = 108 degrees.

Each white hexagon has six angles that are equal in measure. Therefore, each angle in a white hexagon measures:

(angle measure) = (180(6-2))/6 = 120 degrees.

Answer:

just do what the guy above me did

Step-by-step explanation:

i checked its correct

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Answer: Option C, (x - 4)(x - 5)

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Given:  [tex]\textsf{x}^2\textsf{ - 9x + 20}[/tex]

Find:  [tex]\textsf{Determine the factored form}[/tex]

Solution: In order to factor the given equation, we need to first determine two numbers which add up to -9 and multiply to become 20.  We can think of the factors of 20 which would add up to -9 and the one that matches that description would be -5 and -4.  These two numbers multiply to become 20 and combine to become -9.  Now that we have that information, we can break up the quadratic into two separate roots using the two numbers that we found.  

Therefore, the answer would be Option C, (x - 4)(x - 5).

The coordinates of B is (2, -4).

The coordinates of C is (-2, 4).

The coordinates of D is (5, 8).

The coordinates of E is (-2, -4).

In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). Therefore, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

For a reflection over the x-axis, the new coordinates of A is given by:

(x, y)            →      (x, -y)

A (2, 4)      →      (2, -(4)) = B (2, -4)

For a reflection over the y-axis, the new coordinates of A is given by:

(x, y)            →      (-x, y)

A (2, 4)      →      (-(2), 4) = C (-2, 4)

By applying a translation, the new coordinates of A is given by:

(x, y)            →      (x + 3, y + 4)

A (2, 4)      →      (2 + 3, 4 + 4) = D (5, 8)

By applying a rotation 180° clockwise, the new coordinates of A is given by:

(x, y)            →      (-x, -y)

A (2, 4)      →      (-(2), -(4)) = E (-2, -4)

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By answering the presented question using inequality, , we may conclude that Therefore, the equation of the line passing through the points (1,2) and (2,3) is

An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

[tex]y-ylm(x-x1) = \\m = (y^2 - y1)/(x^2 − x^1) \\m = (3-2)/(2-1) = 1\\ m = y-2=1\\(x-1) y-2=x-1\\y = x+1[/tex]

Therefore, the equation of the line passing through the points (1,2) and (2,3) is

D) y=x+1

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A ship sails from port a, on a bearing of 050, to port b which is 80km to the east of a. it then sails on a bearing of 062 for 72km until it reaches pot c. West is 270 degrees. Hence Answer would be 80 km.

Answer:

-1

Step-by-step explanation:

The value of x, the missing side which is the hypotenuse, is approximately 24.85 units.

To solve this problem, we can use the trigonometric function of sine, since we know the opposite side and we want to find the hypotenuse.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:

sin(θ) = opposite/hypotenuse

In this case, θ is the angle 75 degrees, the opposite side is 24, and we want to find the hypotenuse x:

sin(75°) = 24/x

To solve for x, we can cross-multiply:

x * sin(75°) = 24

Then, we can divide both sides by sin(75°):

x = 24 / sin(75°)

Using a calculator, we get:

x = 24.85 units

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Answer: 9

Step-by-step explanation:

Let's first represent the given information in the form of an equation. We know that the long sleeve t-shirts (x) cost $27 each, and the short sleeve t-shirts (y) cost $20 each. Elijah collected $543 in total. So we can write the equation as:

27x + 20y = 543

We also know that Elijah sold 15 short sleeve t-shirts (y), so we can plug that value into the equation:

27x + 20(15) = 543

Now, we solve for x:

27x + 300 = 543

Subtract 300 from both sides of the equation:

27x = 243

Now, divide by 27:

x = 9

So Elijah sold 9 long sleeve t-shirts.

Number of long sleeve t shirts that Elijah sell is 9 long sleeve t shirts.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given that,

The long sleeve t-shirts cost $27 each and the short sleeve t-shirts cost $20 each.

He collected a total of $543.

So, we get an equation,

27x + 20y = 543

Also, given that, Elijah sold 15 short sleeve t-shirts.

Substitute y = 15.

27x + (20 × 15) = 543

27x + 300 = 543

27x = 543 - 300

27x = 243

x = 9

Hence Elijah sold 9 long sleeve t shirts.

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To find the number of degrees the minute hand turned from its first position to its second position, we need to find the difference between the two angles formed by the minute and hour hands.

In the first position, the minute hand forms a 46° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 10 and 11, we know that the hour hand has moved 1/6th of the way from 10 to 11, or 30°. Therefore, the angle between the hour hand and the 12:00 position is 120° + 30° = 150°. So the minute hand is 46° away from 150°, or 104°.

In the second position, the minute hand forms an 84° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 11 and 12, we know that the hour hand has moved 1/2 of the way from 10 to 11, or 150°. So the minute hand is 84° away from 150°, or 234°.

To find the number of degrees the minute hand turned, we subtract the two angles: 234° - 104° = 130°.

Therefore, the minute hand turned 130° from its first position to its second position.

The contrapositive of the given statement is: She will not hang out with her friends If she did not get off work early

Given that we have the following statement:

"If she gets off work early, she will hang out with her friends."

The contrapositive of a statement is defined as:

The above means that we have the contrapositive of the given statement to be:

She will not hang out with her friends If she did not get off work early,

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Answer:

a. 58/99

b. 53/90

c. 29/50

Step-by-step explanation:

The correct angle measures of triangle XWZ are m∠x = 55°, m∠w = 125°, m∠z = 125°.  The correct options are A, B and D.

The correct angle measures are m∠x = 55°, m∠w = 125°, m∠z = 125°

The option "m∠w = 55°" and "m∠z = 55°" are incorrect. Because "m∠w = 55°" and "m∠z = 55°" are incorrect is that there is only one angle measurement that can be equal to 55°, which is m∠x. This is because in any triangle, the sum of the interior angles is always 180°. Therefore, if m∠x is 55°, then the sum of the other two angles (m∠w and m∠z) must add up to 125° (i.e., 180° - 55°).

So, if m∠w is 125°, then m∠z must also be 55°, and if m∠z is 125°, then m∠w must be 55°. Hence, the options "m∠w = 55°" and "m∠z = 55°" cannot both be correct at the same time. So, the correct answers are A, B and D.

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_____The given question is incomplete, the complete question is given below:

Which angle measures are correct? select three options. A m∠x = 55°   B m∠w = 125°   C m∠w = 55°   D m∠z = 125°  E m∠z = 55°.

Answer:

A , B , E

Step-by-step explanation:

Just put A , B , D and got it wrong

Answer:

The value of A is 62

Step-by-step explanation:

since it is parallel to C

Answer: present age of father=42

               present age of son=14

Step-by-step explanation:

let x=present age of father

56-x=present age of son

10 yrs ago:

x-10=age of father

56-x-10=46-x=age of son
age of father=8 times age of son

x-10=8(46-x)

x-10=368-8x

9x=378

x=42

56-x=14

present age of father=42

present age of son=14

Answer:

largest angle ≈ 109.6°

Step-by-step explanation:

the largest angle in the triangle is the angle opposite the longest side.

Here that is the angle opposite side of 7.8 cm

let a = 7.8, b = 5.4 , c = 4.1 and A the largest angle , then

cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]

        = [tex]\frac{5.4^2+4.1^2-7.8^2}{2(5.4)(4.1)}[/tex]

        = [tex]\frac{29.16+16.81-60.84}{44.28}[/tex]

       = [tex]\frac{45.97-60.84}{44.28}[/tex]

       = [tex]\frac{-14.87}{44.28}[/tex]

then

A = [tex]cos^{-1}[/tex] ( [tex]\frac{-14.87}{44.28}[/tex] ) ≈ 109.6° ( to 1 decimal place )

Answer:

85.6 square units.

Step-by-step explanation:

The surface area of a rectangular prism is the sum of the areas of all six faces. To find the surface area of the given rectangular prism, we can use the formula:

Surface Area = 2lw + 2lh + 2wh

where "l" is the length, "w" is the width, and "h" is the height.

Substituting the given values, we get:

Surface Area = 2(6.8)(1.6) + 2(6.8)(3.8) + 2(1.6)(3.8)

= 21.76 + 51.68 + 12.16

= 85.6

the surface area of the rectangular prism is 85.6 square units.